How long has the tank been set up for?
What is the ammonia, nitrite, nitrate and pH of the tank water?
How often do you do water changes and how much do you change?
Do you dechlorinate the new water before it is added to the tank?
What sort of filter do you have?
How often and how do you clean the filter?
What other fish are in the tank?
What are you feeding the eel?
Is there any hiding places in the tank for the eel?
Check the water quality and post the ammonia, nitrite, nitrate and pH levels (in numbers) here.
Do a 75% water change and gravel clean the substrate every day for the next 2 weeks or until we work out what is going on. Make sure any new water is free of chlorine/ chloramine before it's added to the tank.